An　analysis　on　the　nonlinear　dynamics　of　a　cantilever　functionally　graded　materials　(FGM)　cylindrical　shell　subjected　to　the　transversal　and　static　in-plane　pre-applied　excitation　is　presented　in　a　thermal　environment.　Material　properties　are　assumed　to　be　temperature-dependent.　Based　on　Reddy＇s　first-order　shell　theory,　the　nonlinear　governing　equations　of　motion　for　the　FGM　cylindrical　shell　are　derived　using　Hamilton＇s　principle.　Galerkin＇s　method　is　utilized　to　discretize　the　governing　partial　equations　to　a　two-degree-of-freedom　nonlinear　system　including　the　quadratic　and　cubic　nonlinear　terms　under　combined　external　excitations.　It　is　desirable　to　choose　a　suitable　mode　function　to　satisfy　the　first　two　modes　of　transverse　nonlinear　oscillations　and　the　boundary　conditions　for　the　cantilever　FGM　cylindrical　shell.　The　effects　of　external　excitations　on　the　internal　resonance　relationship　and　nonlinear　dynamic　response　of　FGM　cylindrical　shell　are　studied.　The　resonant　case　considered　here　is　1:2　internal　resonance.　A　numerical　method　is　used　to　find　the　nonlinear　dynamic　responses　of　the　cantilever　FGM　cylindrical　shell　with　different　volume　fraction　index.　It　is　found　that　the　vibration　amplitudes　are　not　very　sensitive　to　the　value　of　the　volume　fraction　index　in　the　cases　of　1:2　internal　resonance.　With　the　increasing　of　the　volume　fraction　index,　the　value　of　w(1)　and　w(2)　increased　remarkably.　There　is　a　boundary　value　of　the　forcing　amplitude,　which　divides　the　response　into　two　parts　for　the　case　of　different　volume　fraction　index.　One　is　the　multiple　periodic　motion　of　the　FGM　cantilever　cylindrical　shell　and　the　other　is　the　quasi-period　response.　A　larger　value　of　volume　fraction　index　leads　to　a　larger　region　of　quasi-period　response.